Simplify ( square root of -36)/(- square root of 36)

$\frac{\sqrt{- 36}}{- \sqrt{36}}$

Pull out imaginary unit $i$ .

Rewrite $- 36$ as $- 1 (36)$ .

$\frac{\sqrt{- 1 (36)}}{- \sqrt{36}}$

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{36}}{- \sqrt{36}}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{i \cdot \sqrt{36}}{- \sqrt{36}}$

Cancel the common factor of $\sqrt{36}$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{36}}{- \sqrt{36}}$

Rewrite the expression.

$\frac{i}{- 1}$

Move the negative one from the denominator of $\frac{i}{- 1}$ .

$- 1 \cdot i$

Rewrite $- 1 \cdot i$ as $- i$ .

$- i$